Question: Simplify to lowest terms. $\dfrac{75}{120}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 75 and 120? $75 = 3\cdot5\cdot5$ $120 = 2\cdot2\cdot2\cdot3\cdot5$ $\mbox{GCD}(75, 120) = 3\cdot5 = 15$ $\dfrac{75}{120} = \dfrac{5 \cdot 15}{ 8\cdot 15}$ $\hphantom{\dfrac{75}{120}} = \dfrac{5}{8} \cdot \dfrac{15}{15}$ $\hphantom{\dfrac{75}{120}} = \dfrac{5}{8} \cdot 1$ $\hphantom{\dfrac{75}{120}} = \dfrac{5}{8}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{75}{120}= \dfrac{3\cdot25}{3\cdot40}= \dfrac{3\cdot 5\cdot5}{3\cdot 5\cdot8}= \dfrac{5}{8}$